Construction of unipotent Galois extensions and Massey products

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• 作者：J&aacute ; n Min&aacute ; č^a ; ^{minac@uwo.ca" class="auth_mail" title="E-mail the corresponding author} ; Nguyễn Duy T&acirc ; n^a ; ^b ; ^{duytan@math.ac.vn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Explicit Galois extensions ; Massey products
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：2 January 2017
• 年：2017
• 卷：304
• 期：Complete
• 页码：1021-1054
• 全文大小：595 K

文摘

For all primes p   and for all fields, we find a sufficient and necessary condition of the existence of a unipotent Galois extension of degree thmlsrc">text stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S000187081631218X&_mathId=si1.gif&_user=111111111&_pii=S000187081631218X&_rdoc=1&_issn=00018708&md5=72be151e8b463847c666eb8beda15e05" title="Click to view the MathML source">p⁶thContainer hidden">thCode">th altimg="si1.gif" overflow="scroll">p6th>. The main goal of this paper is to describe an explicit construction of such a Galois extension over fields admitting such a Galois extension. This construction is surprising in its simplicity and generality. The problem of finding such a construction has been left open since 2003. Recently a possible solution of this problem gained urgency because of an effort to extend new advances in Galois theory and its relations with Massey products in Galois cohomology.